In the archives, a parent finds a discussion of magic triangles — but the puzzles assigned his daughter go beyond the counting numbers. Doctor Peterson walks through a range
of strategies, from guess-and-check to algebraic.

Given these eight numbers: 1/4, 1/2, 3/4, 1, 1 1/4, 1 1/2, 1 3/4, and
2, place three numbers along each side of a square so that the sum of
the three numbers on each side of the square is equal to 3. Is there
a trick to doing this kind of problem?

In your sock drawer, you have 10 blue socks, 12 white socks, and 6 red
socks that are all mixed together. It is dark and you can't see the
colors of your socks. What is the least number of socks that you have to
pull out to make sure that you will have a matching pair?